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Experiment 8 -The Angular 
Resolution of the Human Eye and 
Visual Acuity. 



Purpose: The purpose of this lab is to study the Angular Resolution of the human eye. 
Introduction 

In Study 1 you are going to determine the smallest object (or separation) that your eyes 
can see at a given distance using a Test Pattern (a distance to size ratio chart). 

In Study 2 you are going to test your visual acuity during daylight and at night. 
Experimental Write up 

Your experimental write-up should include, but not be limited to, the purpose of the lab 
all the data collected in this experiment, the answers to the questions, the tables, graphs 
and analysis outlined in the lab, samples of the calculations you needed to do for your 
analysis, as well as a Conclusion. Include error bars on the data points on your graphs. 
USE PROPER GRAPH PAPER FOR THE GRAPHS! 

Terms you should know and understand: 

□ Angular Resolution 

□ Test Pattern 

□ Optical Instrument 

□ Rayleigh Criteria 

□ Photoreceptor 



Study 1 - Angular Resolution - Seeing Details with the 
Eye 

In Study 1 you are going to determine the smallest object (or separation) that your eyes 
can see at a given distance. 

Our eyes are optical instruments governed by the same rules of physics as telescopes, 
cameras and microscopes. 

One measure of the performance of an optical instrument is its angular resolution. 
Angular resolution refers to the ability to distinguish between two objects located close 
together in the field of view. The finer the resolution, the smaller the angle, the better 
the instrument. 

In this study, rather than directly measuring the angle, you will measure the spacing 
between lines on a Test Pattern that you can see and compare that to the distance to the 
test pattern. In this measure, the higher the ratio, the better your eye's angular resolution. 
A very similar technique is used to calibrate earth observation satellites using ground- 
based Test Patterns. 

The measurements in this Study are made using a test subject and a person recording the 
results. Affix the test pattern to the wall. 

Stand a distance of 10 metres from the Test Pattern. 

Your partner will hold a sheet of paper over the Test Pattern, hiding all but the bottom 
tip. Tell your partner to move the paper slowly up the Test Pattern, keeping the paper 
horizontal. When you start to see the chart lines clearly separated from each other just 
below the paper, tell your partner to hold the paper in place. 

Your partner will read the line spacing printed on the Test Pattern nearest to the top of 
the paper. 

Repeat this measurement at 5 m and 2 metres. 



Dorset Experiment 8 ( 2 ) Optical Resolution 



Table 1 : In your lab notebook make the following Table and fill with your data: 



Distance (m) 


Line Spacing value (mm) 


Distance to size 
ratio 


10 






5 






2 







Table 1: The distance-to-size ratio for your eyes. 

Suppose when you stood 10 metres (10,000 mm) from the test pattern, and were able to 
distinguish the separation of the lines spaced 4.5 mm apart. The distance-to-size ratio for 
your eyes is the distance to the test pattern divided by the line spacing, which for our 
example is 

distance 1 0, 000mm 



size 



4.5mm 
2,200 



1 



Study 1, Question 1 to answer in your lab write up: Calculate the distance-to-size 
ratio for your eyes for the 10 metre (10,000 mm) distance and the 5 metre (5,000 mm) 
distance and the 2 metre (2,000 mm) distances. 

Study 1, Question 2 to answer in your lab write up: How do the 10 metre (10,000 
mm), the 5 metre (5,000 mm) and the 2 metre (2,000 mm) distance-to-size. ratio compare? 
What is the average of the three ratios for your distance-to-size ratio? Use this value in 
the questions in Study 2. 

Graph 1: Graph the distance-to-size ratio as a function of distance for the three 
distances. Fit a best fit power law curve to your data and determine a power law 
relationship. 



Dorset Experiment 8 



(3) 



Optical Resolution 



Study 2 - Vision Acuity Test during the Day and Night 

The distance-to-size ratio for your eyes determine how much detail you can see based on 
distance. If you know the distance to an object you can estimate the size of an object at 
the limit of your eye's resolution. 

Study 2, Question 1 to answer in your lab write up: Using your distance-to-size ratio 
estimate the furthest distance you could be from two lights, separated from 1.0 cm, and 
still resolve them as two lights? 

Study 2, Question 2 to answer in your lab write up: Using your distance-to-size ratio 
estimate the furthest distance you could be from two lights, separated from 30 m, and still 
resolve them as two lights? 

Study 2, Question 3 to answer in your lab write up: Will you be able to distinguish 
two lights separated by 50 cm if you were standing 500 m from them? 

Study 2, Question 4 to answer in your lab write up: An automobile has headlights 
placed 1.5 m apart. If the car were driving towards you at night, how close do you have 
to be for you to tell it was a car and not a motorcycle. 

Study 2, Question 5 to answer in your lab write up: The average distance from the 
earth to the moon is 3.84 x 10 m. Using your distance-to-size ratio estimate the size of 
the smallest crater you can resolve with your eyes? 

Study 2, Question 6 to answer in your lab write up: The human eye is a sphere 1 .0 cm 
in radius. Draw a schematic of two similar triangles one with the external distance-to-size 
ratio and one with the projection within the human eye. Using your average distance-to- 
size ratio, estimate the internal angular resolution within the eye and an order of 
magnitude for the size and spacing of photoreceptors within your eye? 

Study 2, Question 7 to answer in your lab write up: Research the average spacing of 
the photoreceptors in the human eye and compare your estimate from question 6. How 
does your estimate for the size of the photoreceptors in the human eye compare to the 
Rayleigh Criteria at the frequency of yellow light? 

Study 2, Question 7 to answer in your lab write up: What is the fraction difference 
between your measured angular resolution, compared to the Rayleigh Criteria for yellow 
light? 

Dorset Experiment 8 ( 4 ) Optical Resolution 



\ 



^> 



6.0 mm 




^ 



chart for measuring the distance- to- size ratio. 



■^ 



Dorset Experiment 8 



(5) 



Optical Resolution